Cue PH brainiacs - logic puzzle!

[gasblaster]

You are on a TV game show. The main prize is a car. You have to choose between three doors. Behind one of the doors is the car. Behind the other two doors are goats. You are asked to choose your door. You choose your door, but the host does not open it. The host then opens one of the other doors (that you did not pick) to reveal a goat. The host then gives you one final chance to change your mind about which door you want. Your choice is to stick with your original choice, or to pick the other unopened door. What should you do? And why?




this is taken from an amazing book called 'the curious incident of the dog in the night-time' by mark haddon, vintage, 2004

[gasblaster]

apparently you should always switch and this is the reason:

3 doors:

door 1 = goat. Stick with door 1 = get a goat. Change = get a car
door 2 = goat. Stick with door 2 = get a goat. Change = get a car
door 3 = car. Stick with door 3 = get a car. Change = get a goat

Note that if you chose a goat door (1&2), if you change you get a car because the other goat has already been shown by the host.

So, you stick = 2/3 chance of getting a goat
you change = 2/3 chance of getting a car



>> Edited by gasblaster on Friday 9th December 08:57

[gasblaster]

gasblaster said:

you should always switch and this is the reason: 3 doors: door 1 = goat. Stick with door 1 = get a goat. Change = get a car door 2 = goat. Stick with door 2 = get a goat. Change = get a car door 3 = car. Stick with door 3 = get a car. Change = get a goat Note that if you originally chose a goat door (1&2), if you change you get a car because the other goat has already been shown by the host. So, you stick = 2/3 chance of getting a goat you change = 2/3 chance of getting a car >> Edited by gasblaster on Friday 9th December 08:57

reposted for the benefit of those who can't be ar.. don't have the time to read all previous posts

[gasblaster]

Cristo montado en bicicleta!

The plane does not takeoff as there is no airspeed. You are using flawed logic as per the following example:

The Hare and the Tortoise have a Race:

Tortoise has the traditional head start.
When the hare gets to where the tortoise was (call this T), the tort will have moved some way ahead (T+n)
When the hare gets to this new place (T+n), the tort will have moved a tiny bit further ahead and is now at (T+n+n/y). And so on. Whenever the big-eared thing catches the shelly thing, the latter will have moved a teeny weeny bit further ahead. Ergo, the hare can never overtake the tortoise.

[gasblaster]

Cue U turn coming up!

I have just read the original plane /conveyor question and (in spite of my previous posts) the plane would definitely take off. As they say in exams, always best to read the question!

I think we ought to take a vote on it - all those in favour of the plane taking off raise their hand!

[Gasblaster]

For those who don't get the plane taking off thing, pretend the conveyor belt is not a conveyor belt but a sheet of ice. Same thing applies - a car would just wheelspin and stay put, but a plane would take off in the normal way (assuming it could go in a straight line of course).

[Gasblaster]

boiler said:

So if these jets are producing sooooo much thrust that the plane will take off anyway, how does the friction between the tires and the ground hold this immense thrust prior to take off?

Er, that would be the throttle then. And the brakes. Same as a car.

>> Edited by Gasblaster on Tuesday 13th December 15:02

[Gasblaster]

boiler said:

Gasblaster said: boiler said: So if these jets are producing sooooo much thrust that the plane will take off anyway, how does the friction between the tires and the ground hold this immense thrust prior to take off? Er, that would be the throttle then. And the brakes. Same as a car. >> Edited by Gasblaster on Tuesday 13th December 15:02 And if you go to somewhere like London City airport, because of limited runway space, they put the brakes on, throttle up to (around 85% i believe) and then let the brakes off, so that they do not waste the space. This is exactly what would happen in a car, but then we have accepted that the car would remain stationary.

A car remains stationary because its forward motive force is applied to the ground, which in this case is moving backwards and cancelling it out.

A plane takes off because its forward motive force is applied to the air, which is not affected by the ground (conveyor) moving backwards. See my ice example above.

[GasBlaster]

JonRB said:

dieseljohn said: I'm utterly sick of this now, talk about circular arguements. Bottom line is I agree the plane will take off but I still hold that the question is badly worded and gives insufficient information. I agree. Group hug everyone, m'kay?

The plane won't take off it it is a Gypsy Moth on floats (not wheels), or a revolutionary new plane in which the engine drives the wheels instead of a propeller!

[GasBlaster]

Exige46 said:

But - instantaneously the conveyor counteracts - in fact so quickly that the aeroplane does not actually move in relation to the surrounding air. Cheers

And that is the nub, how is a conveyor belt going to counteract the force of the engine? All the conveyor will do is act on the tyres, which will just spin the wheels, its force is not transmitted to the rest of the plane.

I should hand that degree back mate

[GasBlaster]

gorvid said:

So the relationship between the wheels and the conveyor belt is limited, in that it does not affect the aircraft (force not passed on).... If this was done with a car it would remain still (yes?) (hence the 'no airspeed' argument) But because of the propulsion of the aircraft, it moves along the 'runway' as normal...just that the wheels (and only the wheels) are going ballistic to keep up with the converor belt...?

By Jove I think he's got it!